On the representability of the biuniform matroid
Author
Ball, Simeon
Padró, Carles
Weiner, Zsuzsa
Xing, Chaoping
Date of Issue
2013School
School of Physical and Mathematical Sciences
Version
Published version
Abstract
Every biuniform matroid is representable over all sufficiently large fields. But it is not
known exactly over which finite fields they are representable, and the existence of efficient methods
to find a representation for every given biuniform matroid has not been proved. The interest of these
problems is due to their implications to secret sharing. The existence of efficient methods to find
representations for all biuniform matroids is proved here for the first time. The previously known
efficient constructions apply only to a particular class of biuniform matroids, while the known general
constructions were not proved to be efficient. In addition, our constructions provide in many cases
representations over smaller finite fields.
Subject
DRNTU::Science::Mathematics::Discrete mathematics
Type
Journal Article
Series/Journal Title
SIAM journal on discrete mathematics
Rights
© 2013 Society for Industrial and Applied Mathematics (SIAM). This paper was published in SIAM Journal on Discrete Mathematics and is made available as an electronic reprint (preprint) with permission of SIAM. The paper can be found at the following official DOI: [http://dx.doi.org/10.1137/120886960]. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.
Collections
http://dx.doi.org/10.1137/120886960
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